How to construct a moebius loop using bezier curves
If you have activated the Add mesh: Extra objects, you can use the XYZ surface to create a shape that looks like your avatar. The parameter you'll want to experiment with in the image below, is the 1.5. It controls the size of the inner loop. The 2 controls the number of loops.
I used the formula for an epicycloid (http://en.wikipedia.org/wiki/Epicycloid) and modified it slightly, to give it depth.
Once it looks good, convert it to a curve and put a bevel on it.


EDIT: I realise that this isn't exactly what you wanted to do, but if you add bars between the loops, it should pretty accurately reproduce the kind of image you want.